The impact of halo concentration on the Sunyaev Zel'dovich effect signal from massive galaxy clusters

The Sunyaev Zel'dovich (SZ) effect is sensitive to the pressure of ionized gas inside galaxy clusters, which is in turn controlled largely by the gravitational potential of the cluster. Changing the concentration parameter describing the cluster mass distribution impacts the gravitational potential and thus the cluster SZ signal, with implications for cosmological and other analyses of SZ-selected clusters. We investigate the concentration-SZ relation in theory and simulations. We find that the impact of concentration on the inner SZ profile ($R \lesssim 0.75 R_{200c}$) can be captured with standard polytropic gas models. However, we find that such models do a poor job of reproducing the outer SZ profiles ($R \gtrsim 0.75 R_{200c}$) and the relation between the integrated SZ signal, $Y$, and concentration. This disagreement results from a sharp truncation of the gas pressure profile near the splashback radius, likely caused by virial shocks. We develop a simple description of the truncation that leads to a good match with the simulated SZ profiles out to several $R_{200c}$ for clusters of varying mass and concentration, and that also accurately predicts the concentration-$Y$ relationship. Finally, we determine how inference of the linear bias parameter and splashback radius for SZ-selected clusters can be biased by ignoring the concentration dependence of the SZ signal, finding that bias to the former is essentially negligible, while bias to the latter can be as much as 2\%.